Continuity of magnetic fields

The magnetic field intensity H and the magnetic flux density B are included in the amount representing the magnetic field. In a vacuum, mid-air or when using nonmagnetic material such as plastic or wood, the two quantities have a proportional relationship given by:
B=_μ0H
where _μ0 is called permeability in free space. Among magnetic materials such as ferrous materials and permanent magnets, the relationship between B and H is complicated and shows hysteresis. However, at the boundary where a magnetic material and a nonmagnetic material, or another magnetic material, come into contact with each other, the tangential component H∥ of the magnetic field intensity H and the perpendicular component B_⊥ of the magnetic flux density are continuous. That is:
H_∥1 = H_∥2    B_⊥1 = B_⊥2
These two relationships are set as important laws for designing motors.
The former is derived from Ampere's round-trip integration theorem ∫H・dl=I established in 1820, and the latter is derived from Gauss' theorem divB=0 established in 1829.